A man purchased a table and a chair for Rs 2000 He sold the table at a profit of 20% and the chair a a profit of 30%. His total profit was 23%. Find the cost price of the table.

Options

A. Rs1400
B. Rs600
C. Rs1100
D. Rs1200

Answer

To solve the problem step by step, we will use the information provided to find the cost price of the table.

### Step 1: Understand the total cost price
The total cost price of the table and chair is given as Rs 2000.

### Step 2: Calculate the total profit
The total profit percentage is given as 23%. Therefore, the total profit can be calculated as:
\[ \text{Total Profit} = \text{Total Cost Price} \times \frac{\text{Profit Percentage}}{100} = 2000 \times \frac{23}{100} = 460 \text{ Rs} \]

### Step 3: Calculate the total selling price
The total selling price can be calculated by adding the total profit to the total cost price:
\[ \text{Total Selling Price} = \text{Total Cost Price} + \text{Total Profit} = 2000 + 460 = 2460 \text{ Rs} \]

### Step 4: Let the cost price of the table be \( x \) and the cost price of the chair be \( 2000 - x \)
We denote the cost price of the table as \( x \) and the cost price of the chair as \( 2000 - x \).

### Step 5: Calculate the selling prices based on profit percentages
The selling price of the table at a profit of 20% is:
\[ \text{Selling Price of Table} = x + 0.2x = 1.2x \]
The selling price of the chair at a profit of 30% is:
\[ \text{Selling Price of Chair} = (2000 - x) + 0.3(2000 - x) = 1.3(2000 - x) \]

### Step 6: Set up the equation for total selling price
The total selling price is the sum of the selling prices of the table and the chair:
\[ 1.2x + 1.3(2000 - x) = 2460 \]

### Step 7: Simplify the equation
Expanding the equation:
\[ 1.2x + 1.3 \times 2000 - 1.3x = 2460 \]
\[ 1.2x + 2600 - 1.3x = 2460 \]
Combining like terms:
\[ -0.1x + 2600 = 2460 \]

### Step 8: Solve for \( x \)
Rearranging the equation gives:
\[ -0.1x = 2460 - 2600 \]
\[ -0.1x = -140 \]
Dividing both sides by -0.1:
\[ x = \frac{-140}{-0.1} = 1400 \]

### Step 9: Conclusion
The cost price of the table is Rs 1400.

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